Self-Driving Car Engineer Nanodegree

Deep Learning

Project: Build a Traffic Sign Recognition Classifier

In this notebook, a template is provided for you to implement your functionality in stages, which is required to successfully complete this project. If additional code is required that cannot be included in the notebook, be sure that the Python code is successfully imported and included in your submission if necessary.

Note: Once you have completed all of the code implementations, you need to finalize your work by exporting the iPython Notebook as an HTML document. Before exporting the notebook to html, all of the code cells need to have been run so that reviewers can see the final implementation and output. You can then export the notebook by using the menu above and navigating to \n", "File -> Download as -> HTML (.html). Include the finished document along with this notebook as your submission.

In addition to implementing code, there is a writeup to complete. The writeup should be completed in a separate file, which can be either a markdown file or a pdf document. There is a write up template that can be used to guide the writing process. Completing the code template and writeup template will cover all of the rubric points for this project.

The rubric contains "Stand Out Suggestions" for enhancing the project beyond the minimum requirements. The stand out suggestions are optional. If you decide to pursue the "stand out suggestions", you can include the code in this Ipython notebook and also discuss the results in the writeup file.

Note: Code and Markdown cells can be executed using the Shift + Enter keyboard shortcut. In addition, Markdown cells can be edited by typically double-clicking the cell to enter edit mode.


Step 0: Load The Data

In [4]:
# Load pickled data
import pickle

# TODO: Fill this in based on where you saved the training and testing data

training_file = './train.p'
validation_file= './valid.p'
testing_file = './test.p'

with open(training_file, mode='rb') as f:
    train = pickle.load(f)
with open(validation_file, mode='rb') as f:
    valid = pickle.load(f)
with open(testing_file, mode='rb') as f:
    test = pickle.load(f)
    
X_train, y_train = train['features'], train['labels']
X_valid, y_valid = valid['features'], valid['labels']
X_test, y_test = test['features'], test['labels']

Step 1: Dataset Summary & Exploration

The pickled data is a dictionary with 4 key/value pairs:

  • 'features' is a 4D array containing raw pixel data of the traffic sign images, (num examples, width, height, channels).
  • 'labels' is a 1D array containing the label/class id of the traffic sign. The file signnames.csv contains id -> name mappings for each id.
  • 'sizes' is a list containing tuples, (width, height) representing the original width and height the image.
  • 'coords' is a list containing tuples, (x1, y1, x2, y2) representing coordinates of a bounding box around the sign in the image. THESE COORDINATES ASSUME THE ORIGINAL IMAGE. THE PICKLED DATA CONTAINS RESIZED VERSIONS (32 by 32) OF THESE IMAGES

Complete the basic data summary below. Use python, numpy and/or pandas methods to calculate the data summary rather than hard coding the results. For example, the pandas shape method might be useful for calculating some of the summary results.

Provide a Basic Summary of the Data Set Using Python, Numpy and/or Pandas

In [5]:
### Replace each question mark with the appropriate value. 
### Use python, pandas or numpy methods rather than hard coding the results

# TODO: Number of training examples
n_train = len(X_train)

# TODO: Number of validation examples
#n_validation = len(X_valid)

# TODO: Number of testing examples.
n_test = len(X_test)

# TODO: What's the shape of an traffic sign image?
image_shape = X_train[0].shape

# TODO: How many unique classes/labels there are in the dataset.
n_classes = len(set(y_train))

print("Number of training examples =", n_train)
print("Number of validation examples =", len(X_valid))
print("Number of testing examples =", n_test)
print("Image data shape =", image_shape)
print("Number of classes =", n_classes)
Number of training examples = 34799
Number of validation examples = 4410
Number of testing examples = 12630
Image data shape = (32, 32, 3)
Number of classes = 43

Include an exploratory visualization of the dataset

Visualize the German Traffic Signs Dataset using the pickled file(s). This is open ended, suggestions include: plotting traffic sign images, plotting the count of each sign, etc.

The Matplotlib examples and gallery pages are a great resource for doing visualizations in Python.

NOTE: It's recommended you start with something simple first. If you wish to do more, come back to it after you've completed the rest of the sections. It can be interesting to look at the distribution of classes in the training, validation and test set. Is the distribution the same? Are there more examples of some classes than others?

In [6]:
### Data exploration visualization code goes here.
### Feel free to use as many code cells as needed.
import matplotlib.pyplot as plt
import pandas as pd
import random
import numpy as np
import cv2
# Visualizations will be shown in the notebook.
%matplotlib inline

def getSignNames():
    return pd.read_csv('./signnames.csv').values

def plotImages(X, y, examples_per_sign=15, squeeze=False, cmap=None):
    samples_per_sign = np.bincount(y)
    for sign in getSignNames():
        print("{0}. {1} - Samples: {2}".format(sign[0], sign[1], samples_per_sign[sign[0]]))
        sample_indices = np.where(y==sign[0])[0]
        random_samples = random.sample(list(sample_indices), examples_per_sign)
        fig = plt.figure(figsize = (examples_per_sign, 1))
        fig.subplots_adjust(hspace = 0, wspace = 0)
        for i in range(examples_per_sign):
            image = X[random_samples[i]]
            axis = fig.add_subplot(1,examples_per_sign, i+1, xticks=[], yticks=[])
            if squeeze: image = image.squeeze()
            if cmap == None: axis.imshow(image)
            else: axis.imshow(image.squeeze(), cmap=cmap)
        plt.show()
In [7]:
plotImages(X_train, y_train)
0. Speed limit (20km/h) - Samples: 180
1. Speed limit (30km/h) - Samples: 1980
2. Speed limit (50km/h) - Samples: 2010
3. Speed limit (60km/h) - Samples: 1260
4. Speed limit (70km/h) - Samples: 1770
5. Speed limit (80km/h) - Samples: 1650
6. End of speed limit (80km/h) - Samples: 360
7. Speed limit (100km/h) - Samples: 1290
8. Speed limit (120km/h) - Samples: 1260
9. No passing - Samples: 1320
10. No passing for vehicles over 3.5 metric tons - Samples: 1800
11. Right-of-way at the next intersection - Samples: 1170
12. Priority road - Samples: 1890
13. Yield - Samples: 1920
14. Stop - Samples: 690
15. No vehicles - Samples: 540
16. Vehicles over 3.5 metric tons prohibited - Samples: 360
17. No entry - Samples: 990
18. General caution - Samples: 1080
19. Dangerous curve to the left - Samples: 180
20. Dangerous curve to the right - Samples: 300
21. Double curve - Samples: 270
22. Bumpy road - Samples: 330
23. Slippery road - Samples: 450
24. Road narrows on the right - Samples: 240
25. Road work - Samples: 1350
26. Traffic signals - Samples: 540
27. Pedestrians - Samples: 210
28. Children crossing - Samples: 480
29. Bicycles crossing - Samples: 240
30. Beware of ice/snow - Samples: 390
31. Wild animals crossing - Samples: 690
32. End of all speed and passing limits - Samples: 210
33. Turn right ahead - Samples: 599
34. Turn left ahead - Samples: 360
35. Ahead only - Samples: 1080
36. Go straight or right - Samples: 330
37. Go straight or left - Samples: 180
38. Keep right - Samples: 1860
39. Keep left - Samples: 270
40. Roundabout mandatory - Samples: 300
41. End of no passing - Samples: 210
42. End of no passing by vehicles over 3.5 metric tons - Samples: 210
In [8]:
# plot the histogram
plt.hist(y_train, bins = n_classes)
plt.xlim(xmax=n_classes-1)
plt.show()

Step 2: Design and Test a Model Architecture

Design and implement a deep learning model that learns to recognize traffic signs. Train and test your model on the German Traffic Sign Dataset.

The LeNet-5 implementation shown in the classroom at the end of the CNN lesson is a solid starting point. You'll have to change the number of classes and possibly the preprocessing, but aside from that it's plug and play!

With the LeNet-5 solution from the lecture, you should expect a validation set accuracy of about 0.89. To meet specifications, the validation set accuracy will need to be at least 0.93. It is possible to get an even higher accuracy, but 0.93 is the minimum for a successful project submission.

There are various aspects to consider when thinking about this problem:

  • Neural network architecture (is the network over or underfitting?)
  • Play around preprocessing techniques (normalization, rgb to grayscale, etc)
  • Number of examples per label (some have more than others).
  • Generate fake data.

Here is an example of a published baseline model on this problem. It's not required to be familiar with the approach used in the paper but, it's good practice to try to read papers like these.

Pre-process the Data Set (normalization, grayscale, etc.)

Minimally, the image data should be normalized so that the data has mean zero and equal variance. For image data, (pixel - 128)/ 128 is a quick way to approximately normalize the data and can be used in this project.

Other pre-processing steps are optional. You can try different techniques to see if it improves performance.

Use the code cell (or multiple code cells, if necessary) to implement the first step of your project.

In [9]:
### Preprocess the data here. It is required to normalize the data. Other preprocessing steps could include 
### converting to grayscale, etc.
### Feel free to use as many code cells as needed.
#import cv2
def getGrayScale(img):
    YCrCb = cv2.cvtColor(img, cv2.COLOR_RGB2YCrCb)
    return np.resize(YCrCb[:,:,0], (32,32,1))

def normalizeImage(img):
    a = -0.5
    b = 0.5
    minimum = 0
    maximum = 255
    return a + ((img - minimum) * (b - a)) / (maximum - minimum)

def preprocessImages(images):
    ret_array = []
    for img in images:
        ret_array.append(normalizeImage(getGrayScale(img)))
    return ret_array

X_train = preprocessImages(X_train)
X_valid = preprocessImages(X_valid)
X_test = preprocessImages(X_test)
In [10]:
plotImages(X_train, y_train, squeeze = True, cmap = 'gray')
0. Speed limit (20km/h) - Samples: 180
1. Speed limit (30km/h) - Samples: 1980
2. Speed limit (50km/h) - Samples: 2010
3. Speed limit (60km/h) - Samples: 1260
4. Speed limit (70km/h) - Samples: 1770
5. Speed limit (80km/h) - Samples: 1650
6. End of speed limit (80km/h) - Samples: 360
7. Speed limit (100km/h) - Samples: 1290
8. Speed limit (120km/h) - Samples: 1260
9. No passing - Samples: 1320
10. No passing for vehicles over 3.5 metric tons - Samples: 1800
11. Right-of-way at the next intersection - Samples: 1170
12. Priority road - Samples: 1890
13. Yield - Samples: 1920
14. Stop - Samples: 690
15. No vehicles - Samples: 540
16. Vehicles over 3.5 metric tons prohibited - Samples: 360
17. No entry - Samples: 990
18. General caution - Samples: 1080
19. Dangerous curve to the left - Samples: 180
20. Dangerous curve to the right - Samples: 300
21. Double curve - Samples: 270
22. Bumpy road - Samples: 330
23. Slippery road - Samples: 450
24. Road narrows on the right - Samples: 240
25. Road work - Samples: 1350
26. Traffic signals - Samples: 540
27. Pedestrians - Samples: 210
28. Children crossing - Samples: 480
29. Bicycles crossing - Samples: 240
30. Beware of ice/snow - Samples: 390
31. Wild animals crossing - Samples: 690
32. End of all speed and passing limits - Samples: 210
33. Turn right ahead - Samples: 599
34. Turn left ahead - Samples: 360
35. Ahead only - Samples: 1080
36. Go straight or right - Samples: 330
37. Go straight or left - Samples: 180
38. Keep right - Samples: 1860
39. Keep left - Samples: 270
40. Roundabout mandatory - Samples: 300
41. End of no passing - Samples: 210
42. End of no passing by vehicles over 3.5 metric tons - Samples: 210

Model Architecture

In [11]:
### Define your architecture here.
### Feel free to use as many code cells as needed.
import os
import tensorflow as tf
from tensorflow.contrib.layers import flatten
from sklearn.utils import shuffle

def LeNet(x, num_labels):
    # Hyperparameters
    mu = 0
    sigma = 0.1
    
    # Convolutional Layer. Input = 32x32x1. Output = 28x28x48.
    conv1_W = tf.Variable(tf.truncated_normal(shape=(5, 5, 1, 48), mean = mu, stddev = sigma))
    conv1_b = tf.Variable(tf.zeros([48]))
    conv1 = tf.nn.conv2d(x, conv1_W, strides=[1, 1, 1, 1], padding='VALID') + conv1_b
    conv1 = tf.nn.relu(conv1)

    # Max Pooling. Input = 28x28x48. Output = 14x14x48.
    conv1 = tf.nn.max_pool(conv1, ksize=[1, 2, 2, 1], strides=[1, 2, 2, 1], padding='VALID')

    # Convolutional Layer. Output = 10x10x96.
    conv2_W = tf.Variable(tf.truncated_normal(shape=(5, 5, 48, 96), mean = mu, stddev = sigma))
    conv2_b = tf.Variable(tf.zeros([96]))
    conv2 = tf.nn.conv2d(conv1, conv2_W, strides=[1, 1, 1, 1], padding='VALID') + conv2_b
    conv2 = tf.nn.relu(conv2)

    # Max Pooling. Input = 10x10x96. Output = 5x5x96.
    conv2 = tf.nn.max_pool(conv2, ksize=[1, 2, 2, 1], strides=[1, 2, 2, 1], padding='VALID')
    
    # Convolutional Layer. Input = 5x5x96. Output = 3x3x172.
    conv3_W = tf.Variable(tf.truncated_normal(shape=(3, 3, 96, 172), mean = mu, stddev = sigma))
    conv3_b = tf.Variable(tf.zeros([172]))
    conv3 = tf.nn.conv2d(conv2, conv3_W, strides=[1, 1, 1, 1], padding='VALID') + conv3_b
    conv3 = tf.nn.relu(conv3)
    
    # Max Pooling. Input = 3x3x172. Output = 2x2x172.
    conv3 = tf.nn.max_pool(conv3, ksize=[1, 2, 2, 1], strides=[1, 1, 1, 1], padding='VALID')
    
    # Flatten. Input = 2x2x172. Output = 688.
    fc1 = flatten(conv3)
    
    # Fully Connected. Input = 688. Output = 84.
    fc2_W = tf.Variable(tf.truncated_normal(shape=(688 , 84), mean = mu, stddev = sigma))
    fc2_b = tf.Variable(tf.zeros([84]))
    fc2 = tf.nn.xw_plus_b(fc1, fc2_W, fc2_b)
    fc2 = tf.nn.relu(fc2)

    # Fully Connected. Input = 84. Output = 43.
    fc3_W = tf.Variable(tf.truncated_normal(shape=(84, num_labels), mean = mu, stddev = sigma))
    fc3_b = tf.Variable(tf.zeros([num_labels]))
    logits = tf.nn.xw_plus_b(fc2, fc3_W, fc3_b)
    
    return logits

# tf.one_hot() on windows in GPU mode failed with CUDA_ERROR_ILLEGAL_ADDRESS
# https://github.com/tensorflow/tensorflow/issues/6509
def one_hot_workaround(y, num_labels):
    sparse_labels = tf.reshape(y, [-1, 1])
    derived_size = tf.shape(sparse_labels)[0]
    indices = tf.reshape(tf.range(0, derived_size, 1), [-1, 1])
    concated = tf.concat(1, [indices, sparse_labels])
    outshape = tf.concat(0, [tf.reshape(derived_size, [1]), tf.reshape(num_labels, [1])])
    return tf.sparse_to_dense(concated, outshape, 1.0, 0.0)

x = tf.placeholder(tf.float32, (None, 32, 32, 1))
y = tf.placeholder(tf.int32, (None))

# y_one_hot = tf.one_hot(y, n_classes)
y_one_hot = one_hot_workaround(y, n_classes)
logits = LeNet(x, n_classes)
cross_entropy = tf.nn.softmax_cross_entropy_with_logits(logits, y_one_hot)
loss_operation = tf.reduce_mean(cross_entropy)
optimizer = tf.train.AdamOptimizer(learning_rate = 0.001)
training_operation = optimizer.minimize(loss_operation)

Train, Validate and Test the Model

A validation set can be used to assess how well the model is performing. A low accuracy on the training and validation sets imply underfitting. A high accuracy on the training set but low accuracy on the validation set implies overfitting.

In [12]:
### Train your model here.
### Calculate and report the accuracy on the training and validation set.
### Once a final model architecture is selected, 
### the accuracy on the test set should be calculated and reported as well.
### Feel free to use as many code cells as needed.
correct_prediction = tf.equal(tf.argmax(logits, 1), tf.argmax(y_one_hot, 1))
accuracy_operation = tf.reduce_mean(tf.cast(correct_prediction, tf.float32))
saver = tf.train.Saver()

EPOCHS = 35
BATCH_SIZE = 128

def evaluate(X_data, y_data):
    num_examples = len(X_data)
    total_accuracy = 0
    sess = tf.get_default_session()
    for offset in range(0, num_examples, BATCH_SIZE):
        batch_x, batch_y = X_data[offset:offset+BATCH_SIZE], y_data[offset:offset+BATCH_SIZE]
        accuracy = sess.run(accuracy_operation, feed_dict={x: batch_x, y: batch_y})
        total_accuracy += (accuracy * len(batch_x))
    return total_accuracy / num_examples


with tf.Session() as sess:
    sess.run(tf.global_variables_initializer())
    num_examples = len(X_train)

    print("Training...")
    for i in range(EPOCHS):
        print("EPOCH {} ... ".format(i+1), end='')
        X_train, y_train = shuffle(X_train, y_train)
        for offset in range(0, num_examples, BATCH_SIZE):
            end = offset + BATCH_SIZE
            batch_x, batch_y = X_train[offset:end], y_train[offset:end]
            sess.run(training_operation, feed_dict={x: batch_x, y: batch_y})
        validation_accuracy = evaluate(X_valid, y_valid)
        print("Validation Accuracy = {:.3f}".format(validation_accuracy))
        
    saver.save(sess, './lenet')
    print("Model saved")
Training...
EPOCH 1 ... Validation Accuracy = 0.842
EPOCH 2 ... Validation Accuracy = 0.901
EPOCH 3 ... Validation Accuracy = 0.921
EPOCH 4 ... Validation Accuracy = 0.938
EPOCH 5 ... Validation Accuracy = 0.919
EPOCH 6 ... Validation Accuracy = 0.942
EPOCH 7 ... Validation Accuracy = 0.947
EPOCH 8 ... Validation Accuracy = 0.955
EPOCH 9 ... Validation Accuracy = 0.942
EPOCH 10 ... Validation Accuracy = 0.964
EPOCH 11 ... Validation Accuracy = 0.952
EPOCH 12 ... Validation Accuracy = 0.960
EPOCH 13 ... Validation Accuracy = 0.950
EPOCH 14 ... Validation Accuracy = 0.948
EPOCH 15 ... Validation Accuracy = 0.951
EPOCH 16 ... Validation Accuracy = 0.965
EPOCH 17 ... Validation Accuracy = 0.935
EPOCH 18 ... Validation Accuracy = 0.952
EPOCH 19 ... Validation Accuracy = 0.956
EPOCH 20 ... Validation Accuracy = 0.961
EPOCH 21 ... Validation Accuracy = 0.960
EPOCH 22 ... Validation Accuracy = 0.960
EPOCH 23 ... Validation Accuracy = 0.960
EPOCH 24 ... Validation Accuracy = 0.961
EPOCH 25 ... Validation Accuracy = 0.961
EPOCH 26 ... Validation Accuracy = 0.960
EPOCH 27 ... Validation Accuracy = 0.961
EPOCH 28 ... Validation Accuracy = 0.961
EPOCH 29 ... Validation Accuracy = 0.961
EPOCH 30 ... Validation Accuracy = 0.960
EPOCH 31 ... Validation Accuracy = 0.961
EPOCH 32 ... Validation Accuracy = 0.961
EPOCH 33 ... Validation Accuracy = 0.960
EPOCH 34 ... Validation Accuracy = 0.960
EPOCH 35 ... Validation Accuracy = 0.960
Model saved
In [13]:
with tf.Session() as sess:
    saver.restore(sess, tf.train.latest_checkpoint('.'))

    test_accuracy = evaluate(X_test, y_test)
    print("Test Accuracy = {:.3f}".format(test_accuracy))
Test Accuracy = 0.951

Step 3: Test a Model on New Images

To give yourself more insight into how your model is working, download at least five pictures of German traffic signs from the web and use your model to predict the traffic sign type.

You may find signnames.csv useful as it contains mappings from the class id (integer) to the actual sign name.

Load and Output the Images

In [14]:
# Reinitialize and re-import if starting a new kernel here
import matplotlib.pyplot as plt
%matplotlib inline

import tensorflow as tf
import numpy as np
import cv2

print('done')
done
In [15]:
### Load the images and plot them here.
### Feel free to use as many code cells as needed.
### Load the images and plot them here.
### Feel free to use as many code cells as needed.
#reading in an image
import glob
import cv2
import matplotlib.image as mpimg

fig, axs = plt.subplots(2,4, figsize=(4, 2))
fig.subplots_adjust(hspace = .2, wspace=.001)
axs = axs.ravel()

my_images = []

for i, img in enumerate(glob.glob('./my-found-traffic-signs/*x.png')):
    image = cv2.imread(img)
    axs[i].axis('off')
    axs[i].imshow(cv2.cvtColor(image, cv2.COLOR_BGR2RGB))
    my_images.append(image)

my_images = np.asarray(my_images)

my_images_gry = np.sum(my_images/3, axis=3, keepdims=True)

my_images_normalized = (my_images_gry - 128)/128 

print(my_images_normalized.shape)
(8, 32, 32, 1)

Predict the Sign Type for Each Image

In [16]:
### Run the predictions here and use the model to output the prediction for each image.
### Make sure to pre-process the images with the same pre-processing pipeline used earlier.
### Feel free to use as many code cells as needed.
my_labels = [3, 11, 1, 12, 38, 34, 18, 25]


with tf.Session() as sess:
    sess.run(tf.global_variables_initializer())
    saver3 = tf.train.import_meta_graph('./lenet.meta')
    saver3.restore(sess, "./lenet")
    my_accuracy = evaluate(my_images_normalized, my_labels)
    print("Test Set Accuracy = {:.3f}".format(my_accuracy))
Test Set Accuracy = 0.125
In [17]:
 
---------------------------------------------------------------------------
NameError                                 Traceback (most recent call last)
<ipython-input-17-84c1ef100c23> in <module>()
----> 1 draw_images(signs_from_web_proccessed, squeeze=True, cmap='gray')

NameError: name 'draw_images' is not defined

Analyze Performance

In [18]:
 
---------------------------------------------------------------------------
NameError                                 Traceback (most recent call last)
<ipython-input-18-8c5463ee4003> in <module>()
      1 # last example traffic sign is not in training set, set label to 0 to make sure evaluate function works
----> 2 labels[-1] = 0

NameError: name 'labels' is not defined
In [30]:
### Calculate the accuracy for these 5 new images. 
### For example, if the model predicted 1 out of 5 signs correctly, it's 20% accurate on these new images.
import tensorflow as tf
import numpy as np
import cv2

softmax_logits = tf.nn.softmax(logits)
top_k = tf.nn.top_k(softmax_logits, k=3)


with tf.Session() as sess:
    sess.run(tf.global_variables_initializer())
    saver = tf.train.import_meta_graph('./lenet.meta')
    saver.restore(sess, "./lenet")
    my_softmax_logits = sess.run(softmax_logits, feed_dict={x: my_images_normalized})
    my_top_k = sess.run(top_k, feed_dict={x: my_images_normalized})

    
    fig, axs = plt.subplots(len(my_images),4, figsize=(12, 14))
    fig.subplots_adjust(hspace = .4, wspace=.2)
    axs = axs.ravel()

    for i, image in enumerate(my_images):
        axs[4*i].axis('off')
        axs[4*i].imshow(cv2.cvtColor(image, cv2.COLOR_BGR2RGB))
        axs[4*i].set_title('input')
        guess1 = my_top_k[1][i][0]
        index1 = np.argwhere(y_validation == guess1)[0]
        axs[4*i+1].axis('off')
        axs[4*i+1].imshow(X_validation[index1].squeeze(), cmap='gray')
        axs[4*i+1].set_title('top guess: {} ({:.0f}%)'.format(guess1, 100*my_top_k[0][i][0]))
        guess2 = my_top_k[1][i][1]
        index2 = np.argwhere(y_validation == guess2)[0]
        axs[4*i+2].axis('off')
        axs[4*i+2].imshow(X_validation[index2].squeeze(), cmap='gray')
        axs[4*i+2].set_title('2nd guess: {} ({:.0f}%)'.format(guess2, 100*my_top_k[0][i][1]))
        guess3 = my_top_k[1][i][2]
        index3 = np.argwhere(y_validation == guess3)[0]
        axs[4*i+3].axis('off')
        axs[4*i+3].imshow(X_validation[index3].squeeze(), cmap='gray')
        axs[4*i+3].set_title('3rd guess: {} ({:.0f}%)'.format(guess3, 100*my_top_k[0][i][2]))
---------------------------------------------------------------------------
NameError                                 Traceback (most recent call last)
<ipython-input-30-22c20b4dbf1e> in <module>()
     26         axs[4*i].set_title('input')
     27         guess1 = my_top_k[1][i][0]
---> 28         index1 = np.argwhere(y_validation == guess1)[0]
     29         axs[4*i+1].axis('off')
     30         axs[4*i+1].imshow(X_validation[index1].squeeze(), cmap='gray')

NameError: name 'y_validation' is not defined

Output Top 5 Softmax Probabilities For Each Image Found on the Web

For each of the new images, print out the model's softmax probabilities to show the certainty of the model's predictions (limit the output to the top 5 probabilities for each image). tf.nn.top_k could prove helpful here.

The example below demonstrates how tf.nn.top_k can be used to find the top k predictions for each image.

tf.nn.top_k will return the values and indices (class ids) of the top k predictions. So if k=3, for each sign, it'll return the 3 largest probabilities (out of a possible 43) and the correspoding class ids.

Take this numpy array as an example. The values in the array represent predictions. The array contains softmax probabilities for five candidate images with six possible classes. tf.nn.top_k is used to choose the three classes with the highest probability:

# (5, 6) array
a = np.array([[ 0.24879643,  0.07032244,  0.12641572,  0.34763842,  0.07893497,
         0.12789202],
       [ 0.28086119,  0.27569815,  0.08594638,  0.0178669 ,  0.18063401,
         0.15899337],
       [ 0.26076848,  0.23664738,  0.08020603,  0.07001922,  0.1134371 ,
         0.23892179],
       [ 0.11943333,  0.29198961,  0.02605103,  0.26234032,  0.1351348 ,
         0.16505091],
       [ 0.09561176,  0.34396535,  0.0643941 ,  0.16240774,  0.24206137,
         0.09155967]])

Running it through sess.run(tf.nn.top_k(tf.constant(a), k=3)) produces:

TopKV2(values=array([[ 0.34763842,  0.24879643,  0.12789202],
       [ 0.28086119,  0.27569815,  0.18063401],
       [ 0.26076848,  0.23892179,  0.23664738],
       [ 0.29198961,  0.26234032,  0.16505091],
       [ 0.34396535,  0.24206137,  0.16240774]]), indices=array([[3, 0, 5],
       [0, 1, 4],
       [0, 5, 1],
       [1, 3, 5],
       [1, 4, 3]], dtype=int32))

Looking just at the first row we get [ 0.34763842, 0.24879643, 0.12789202], you can confirm these are the 3 largest probabilities in a. You'll also notice [3, 0, 5] are the corresponding indices.

In [31]:
### Print out the top five softmax probabilities for the predictions on the German traffic sign images found on the web. 
### Feel free to use as many code cells as needed.

fig, axs = plt.subplots(8,2, figsize=(9, 19))
axs = axs.ravel()

for i in range(len(my_softmax_logits)*2):
    if i%2 == 0:
        axs[i].axis('off')
        axs[i].imshow(cv2.cvtColor(my_images[i//2], cv2.COLOR_BGR2RGB))
    else:
        axs[i].bar(np.arange(n_classes), my_softmax_logits[(i-1)//2]) 
        axs[i].set_ylabel('Softmax probability')

Project Writeup

Once you have completed the code implementation, document your results in a project writeup using this template as a guide. The writeup can be in a markdown or pdf file.

Note: Once you have completed all of the code implementations and successfully answered each question above, you may finalize your work by exporting the iPython Notebook as an HTML document. You can do this by using the menu above and navigating to \n", "File -> Download as -> HTML (.html). Include the finished document along with this notebook as your submission.


Step 4 (Optional): Visualize the Neural Network's State with Test Images

This Section is not required to complete but acts as an additional excersise for understaning the output of a neural network's weights. While neural networks can be a great learning device they are often referred to as a black box. We can understand what the weights of a neural network look like better by plotting their feature maps. After successfully training your neural network you can see what it's feature maps look like by plotting the output of the network's weight layers in response to a test stimuli image. From these plotted feature maps, it's possible to see what characteristics of an image the network finds interesting. For a sign, maybe the inner network feature maps react with high activation to the sign's boundary outline or to the contrast in the sign's painted symbol.

Provided for you below is the function code that allows you to get the visualization output of any tensorflow weight layer you want. The inputs to the function should be a stimuli image, one used during training or a new one you provided, and then the tensorflow variable name that represents the layer's state during the training process, for instance if you wanted to see what the LeNet lab's feature maps looked like for it's second convolutional layer you could enter conv2 as the tf_activation variable.

For an example of what feature map outputs look like, check out NVIDIA's results in their paper End-to-End Deep Learning for Self-Driving Cars in the section Visualization of internal CNN State. NVIDIA was able to show that their network's inner weights had high activations to road boundary lines by comparing feature maps from an image with a clear path to one without. Try experimenting with a similar test to show that your trained network's weights are looking for interesting features, whether it's looking at differences in feature maps from images with or without a sign, or even what feature maps look like in a trained network vs a completely untrained one on the same sign image.

Combined Image

Your output should look something like this (above)